We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field, meaning that the vorticity is collinear to the velocity. The existence theory is based on multi-parameter bifurcation theory.

中文翻译：

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具有涡度的小振幅双周期水波的存在理论

我们证明了在有限深度的水面上存在具有涡度的三维稳定重力毛细波。波相对于给定的二维晶格是周期性的，相对速度场是贝尔特拉米场，这意味着涡度与速度共线。存在论是基于多参数分岔理论。